Using the meanings of fractions, multiplication and division, and the relationship between multiplication and division, students will understand and explain why the procedures for dividing fractions make sense. They will interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions. These skills can be applied in solving volume problems where the edge lengths have fractional values. By the end of 6th grade, students are expected to fluently (with speed and accuracy) divide multi-digit numbers and compute with multidigit decimals, using the standard algorithms. These skills should be solidified in this unit. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Big Idea
Apply and extend previous understandings of multiplication and division to divide fractions by fractions
Essential Questions:
How do I show that multiplication and division of fractions are related/interconnected?
What strategies do I use to solve problems and how can I explain those to others?
Vocabulary
Algorithm: a step-by-step solution to a problem.
Difference: The amount left after one number is subtracted from another number.
Distributive Property: The sum of two addends multiplied by a number is the sum of the product of each addend and the number.
Dividend: A number that is divided by another number.
Divisor: A number by which another number is to be divided.
Factor: When two or more integers are multiplied, each number is a factor of the product. "To factor" means to write the number or term as a product of its factors.
Greatest Common Factor: The largest factor that two or more numbers have in common.
Least Common Multiple: The smallest multiple (other than zero) that two or more numbers have in common.
Minuend: The number that is to be subtracted from.
Multiple: The product of a given whole number and an integer.
Quotient: A number that is the result of division.
Reciprocal: Two numbers whose product is 1.
Sum: The number you get by adding two or more numbers together
Subtrahend: The number that is to be subtracted.
Product: A number that is the result of multiplication.
Content
Find the greatest common factor of two whole numbers less than or equal to 100
Find the least common multiple of two whole numbers less than or equal to 12
Use the distributive property to express a sum of two whole numbers 1-100 with a
common factor as a multiple of a sum of two whole numbers with no common factor. Interpret and compute quotients of fractions
Solve word problems involving division of fractions by fractions using visual fraction
models and equations to represent the problem.
Fluently divide multi-digit numbers using the standard algorithm
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
Skills Needed
number sense
computation with multi-digit whole numbers and decimals (to hundredths), including
application of order of operations
addition, subtraction, multiplication, and division of common fractions
Investigation 2: Building on Multiplication with Fractions
Standards: 6.EE.A3, 6.NS.A1
P.30-P.46
Investigation 3: Dividing with Fractions
Standards: 6.NS.A1, 6.EE.A2b
P.47-P.64
Investigation 4: Wrapping Up the Operations
Standards: 6.EE.A2, 6.EE.B6, 6.EE.B7
P.65-P.78
Looking Back: Use Your Understanding: Fraction Operations
See above standards
P.79-P.80
Standards
6.NS.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2
Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
Table of Contents
Common Core Learning Standard
Big Idea
Essential Questions:
Vocabulary
Content
Skills Needed
on
Topic
Resources
Arc 1
1-8
1-9
Skills handbook
page 642
1-9
215
242-263
1-9
242-263
1-8
1-9
242-263
4-7
CC-5
74-91
4-7
CC-5
74-91
CC-5
74-91
Arc 2
6-4
Activity Lab 6-3a
233-241
6-4
Activity Lab 6-3a
233-241
6-4
Activity Lab 6-3a
233-241
Activity Lab 6-3a
233-241
CC-10
451-453
Unit Assessments
Part A: Multiple Choice
Part B: Extended Response
Extension:
CMP3: Let's Be Rational
Pages Numbers:
Standards